Relaxation in classical systems

Dear all,

I'd like to specify meaning othe relaxation phenomenon on example in some classical system.
For example in Wiki I found example of dampled oscilator where the relaxation time ( the time is needed for the system to return to the equilibrium fluctuation pattern) add exponential decay to the motion equation of such oscilator

http://en.wikipedia.org/wiki/Relaxat...ced_oscillator


Could some one provide me more quatinely what with such system will be expected in case of increasing (decreasing) of the relaxation time ? What are the examples of the non-exponential terms in different relaxation phenomena?

James